Question

Calculate Mean Deviation about Median

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	$5$	$10$	$20$	$5$	$10$

• A. $7$
• B. $8$
• C. $19$
• D. $9$

Answer 1

Answer: (D)

$9$

We have to calculate the mean deviation about the median of following data:

Class	Mid-Value($x_i$)	$f_i$	Cummulative Frequency	$|x_i-Median|$	$f_i|x_i-Median|$
$0-10$	$5$	$5$	$0+5=5$	$20$	$100$
$10-20$	$15$	$10$	$5+10=15$	$10$	$100$
$20-30$	$25$	$20$	$15+20=35$	$0$	$0$
$30-40$	$35$	$5$	$35+5=40$	$10$	$50$
$40-50$	$45$	$10$	$40+10=50$	$20$	$200$

$N=\sum f_i=50$

Here, $N=50$ , so $\frac{50}{2}=25$ and the cummulative frquency is just greater than $\frac{N}{2}$ is $35$.

Thus, $20-30$ is median class.

$l$=lower limit of median class$=20$

$F$=Cummulative frequency before median class$=15$

Difference between the class=$h=10$

frequency of median class=$f=20$

Median$=l+\frac{\frac{N}{2}-F}{f}\times h=20+\frac{25-15}{20}\times 10=25$

$\sum f_i\times |x_i-Median|=450$

mean deviation about the mean$=\frac{1}{N}\sum f_I\times |x_i-Median|=\frac{1}{50}\times 450=9$